System and method for robust 2D-3D image registration
View Patent ↗A method for registering 2-dimensional (2D) images with 3-dimensional (3D) images includes receiving a 2D reference image and a 3D moving image, initializing a registration parameter matrix that rigidly transforms the domain of the moving image, randomly sampling a set of registration parameter matrices in a neighborhood of the initial registration parameters, estimating a cost function for each of the randomly sampled parameter matrices, calculating a distance from each randomly sampled parameter matrix to the initial registration parameter matrix, calculating a mean shift vector from the estimated cost functions and distance, and updating the initial registration parameter matrix from the mean shift vector.
1. A computer implemented method for registering 2-dimensional (2D) images with 3-dimensional (3D) images, the method performed by the computer comprising the steps of:
receiving a 2D reference image and a 3D moving image;
initializing a registration parameter matrix that rigidly transforms the domain of the moving image;
randomly sampling a set of registration parameter matrices in a neighborhood of the initial registration parameters;
estimating a cost function for each of the randomly sampled parameter matrices;
calculating a distance from each randomly sampled parameter matrix to the initial registration parameter matrix, including calculating d 2 (T i , T i j )=∥log(T i −1 T i j )∥ M 2 , wherein T i is the initial registration parameter matrix, T i j is a randomly sampled parameter matrix, and ∥·∥ M denotes a matrix norm;
calculating a mean shift vector from said estimated cost functions and distance; and
updating said initial registration parameter matrix from said mean shift vector.
2. The method of claim 1 , further comprising repeating said steps of randomly sampling a set of parameters, estimating a cost function, calculating a distance, and calculating a mean shift vector until a magnitude of said mean shift vector is less than a predetermined constant.
3. The method of claim 1 , wherein a cost function for a randomly sampled parameter matrix is determined by applying a randomly sampled parameter matrix to transform the domain of the moving image, and calculating one of a similarity metric or a dissimilarity metric on a 2D projection of the transformed moving image and the reference image.
4. The method of claim 1 , wherein said registration parameter matrix is a 4×4 matrix representing a 3D affine transformation that includes rotation and translation.
5. The method of claim 1 , wherein the mean shift vector is calculated from
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wherein T i is the initial registration parameter matrix, T i j is a randomly sampled parameter matrix, C(T i j ) is the cost function of T i j , d 2 (T i , T i j ) is the distance between T i and T i j , g is the derivative of a kernel function k of bandwidth h, and the sum is over all randomly sampled registration parameter matrices.
6. The method of claim 5 , wherein said initial registration parameter matrix is updated from said mean shift vector according to T i+1 =exp Ti (Δ h (T i )).
7. The method of claim 5 , wherein said kernel function k is a bounded function that satisfies ∫k(∥x∥ 2 )dx=1, ∫∥x∥k(∥x∥ 2 )dx=0, lim ∥x∥→∞ ∥x∥k(∥x∥ 2 )=0, and ∫∥x∥ 2 k(∥x∥ 2 )dx=c k , where c k is a constant and the integrals are over all space.
8. The method of claim 7 , wherein the kernel function is a Gaussian.
9. The method of claim 5 , wherein the bandwidth h of the kernel is determined from a standard deviation of a random distribution used to generate the randomly sampled set of registration parameter matrices.
10. The method of claim 2 , further comprising changing a standard deviation of a random distribution used to generate the randomly sampled set of registration parameter matrices.
11. A computer implemented method for registering 2-dimensional (2D) images with 3-dimensional (3D) images, the method performed by the computer comprising the steps of:
receiving a 2D reference image and a 3D moving image;
initializing a registration parameter matrix that rigidly transforms the domain of the moving image;
randomly sampling a set of registration parameter matrices in a neighborhood of the initial registration parameters;
calculating a mean shift vector from
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wherein T i is the initial registration parameter matrix, T i j is a randomly sampled parameter matrix, C(T i j ) is a cost function of T i j , d 2 (T i , T i j ) is a distance between T i and T i j , g is the derivative of a Gaussian kernel function k of bandwidth h, and the sum is over all randomly sampled registration parameter matrices; and
calculating an updated registration parameter matrix T i+1 from T i+1 =exp Ti (Δ h (T i )).
12. The method of claim 11 , wherein d 2 (T i , T i j )=∥log(T i −1 T i j )∥ M 2 , wherein ∥·∥ M denotes a matrix norm.
13. The method of claim 11 , wherein said cost function C(T i j ) is determined by applying T i j to transform the domain of the moving image, and calculating one of a similarity metric or a dissimilarity metric on a 2D projection of the transformed moving image and the reference image.
14. A program storage device readable by a computer, tangibly embodying a program of instructions executable by the computer to perform the method steps for registering 2-dimensional (2D) images with 3-dimensional (3D) images, the method comprising the steps of:
receiving a 2D reference image and a 3D moving image;
initializing a registration parameter matrix that rigidly transforms the domain of the moving image;
randomly sampling a set of registration parameter matrices in a neighborhood of the initial registration parameters;
estimating a cost function for each of the randomly sampled parameter matrices;
calculating a distance from each randomly sampled parameter matrix to the initial registration parameter matrix, including calculating d 2 (T i , T i j )=∥log(T i −1 T i j )∥ M 2 , wherein T i is the initial registration parameter matrix, T i j is a randomly sampled parameter matrix, and ∥·∥ M denotes a matrix norm;
calculating a mean shift vector from said estimated cost functions and distance; and
updating said initial registration parameter matrix from said mean shift vector.
15. The computer readable program storage device of claim 14 , the method further comprising repeating said steps of randomly sampling a set of parameters, estimating a cost function, calculating a distance, and calculating a mean shift vector until a magnitude of said mean shift vector is less than a predetermined constant.
16. The computer readable program storage device of claim 14 , wherein a cost function for a randomly sampled parameter matrix is determined by applying a randomly sampled parameter matrix to transform the domain of the moving image, and calculating one of a similarity metric or a dissimilarity metric on a 2D projection of the transformed moving image and the reference image.
17. The computer readable program storage device of claim 14 , wherein said registration parameter matrix is a 4×4 matrix representing a 3D affine transformation that includes rotation and translation.
18. The computer readable program storage device of claim 14 , wherein the mean shift vector is calculated from
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wherein T i is the initial registration parameter matrix, T i j is a randomly sampled parameter matrix, C(T i j ) is the cost function of T i j , d 2 (T i , T i j ) is the distance between T i and T i j , g is the derivative of a kernel function k of bandwidth h, and the sum is over all randomly sampled registration parameter matrices.
19. The computer readable program storage device of claim 18 , wherein said initial registration parameter matrix is updated from said mean shift vector according to T i+1 =exp Ti (Δ h (T i )).
20. The computer readable program storage device of claim 18 , wherein said kernel function k is a bounded function that satisfies ∫k(∥k∥ 2 )dx=1, ∫∥x∥k(∥x∥ 2 )dx=0, lim ∥x∥→∞ ∥x∥k(∥x∥ 2 )=0, and ∫∥x∥ 2 k(∥x∥ 2 k(∥x∥ 2 )dx=c k , where c k is a constant and the integrals are over all space.
21. The computer readable program storage device of claim 20 , wherein the kernel function is a Gaussian.
22. The computer readable program storage device of claim 18 , wherein the bandwidth h of the kernel is determined from a standard deviation of a random distribution used to generate the randomly sampled set of registration parameter matrices.
23. The computer readable program storage device of claim 15 , the method further comprising changing a standard deviation of a random distribution used to generate the randomly sampled set of registration parameter matrices.